Gas turbine rotor assembly method

ABSTRACT

Methods of assembling a rotor assembly of a gas turbine engine having a plurality of components. The method comprises, in one aspect, determining a static unbalance force of each component using the mass and the center of mass location, and determining an optimum assembly arrangement minimizing static unbalance forces. Optimal component stacking positions, among other things, may then be established.

TECHNICAL FIELD

The invention relates generally to methods for assembling rotor components and in particular, high speed rotors such as those in gas turbine engines.

BACKGROUND OF THE ART

It is routine for gas turbine engines to have to pass stringent vibration acceptance tests following production. Rotor eccentricities are a main source of engine vibration, and eccentricities can be alleviated by rotor balancing. Balancing is the act of aligning the masses arid rotational centers of the rotor assembly. Complicating matters greatly is the fact that gas turbine, engine rotors typically comprise a plurality of rotors, such as multiple compressor or turbine stages, which are bolted or clamped together. The prior art approaches to rotor balancing have had reasonable success with simple rotors, but not as much with complicated rotors of the type found in gas turbine engines. So, while methods and apparatuses already exist for assisting in gas turbine rotor balancing, errors present in these approaches can tend to be magnified by the complicated rotor designs, and thus present a risk, that an engine will not meet test requirements despite having been balanced according to prior art techniques. If an engine does not pass the vibration acceptance limit, it typically must be disassembled, re-balanced, and reassembled, which wastes time and resources. Accordingly, there is a need to provide improvements to rotor assembly.

SUMMARY

In one aspect, there is provided is a method of assembling a rotor assembly of a gas turbine engine having a plurality of rotor components, the method comprising the steps of: for each rotor component, determining a mass and a location of a center of mass with respect to an axis of rotation of the rotor assembly; using the mass and the location of the center of mass to determine a static unbalance force associated with each rotor component; summing the static unbalance forces of the rotor components to provide a total static unbalance force of the rotor assembly; optimizing an arrangement of rotor components to thereby minimize the total static unbalance force of the rotor assembly; and assembling the rotor using said optimized arrangement of rotor components.

In accordance with another general aspect, there is provided a method of assembling a rotor assembly supported by at least two bearings, the rotor assembly including a plurality of rotor components each having a center of mass spaced-apart at fixed points along an axis of rotation of the rotor assembly, the method comprising the steps of: for an initial assembly of the components, acquiring geometric data indicative of a radial deviation of a center of mass from a datum for each component; acquiring mass data for each component; using the radial deviation and mass data to determine at least one of a total static unbalance force of the rotor assembly and a total static unbalance force at each bearing; determining a set of rotor component stacking positions providing at least one of a minimum total static unbalance force of the rotor assembly and a minimum total static unbalance force at each bearing; assembling the rotor assembly using said set of rotor component stacking positions.

In accordance with a further general aspect of the present invention, there is provided a method of assembling a rotor assembly of a gas turbine engine having a plurality of components, each component having a mass, a center of mass and a plurality possible stacking positions relative to the other components, the method comprising the steps of: determining a static unbalance force vector for each component by using the mass and a location of the center of mass; determining a combination of component stacking positions providing a minimum total static unbalance force for the rotor assembly; and assembling the rotor assembly using said combination of stacking positions.

In accordance with a still Further general aspect, there is provided a method of assembling a rotor assembly of a gas turbine engine having a plurality of rotor components mounted for rotation about an axis of rotation, each rotor component having a mass, a center of mass and multiple possible angular stacking positions with respect to the other rotor components, the method comprising the steps of: for a plurality of said possible stacking positions, determining a position of the center of mass of each of the components relative to the axis of rotation; for a plurality of said possible stacking positions, using the mass of each of the rotor components and respective positions of the centers of mass thereof to determine an associated static unbalance force of each rotor component; selecting a set of said angular stacking positions which provide a minimal total static unbalance force for the rotor assembly; and assembling the rotor assembly using said set of said angular stacking positions for the rotor components.

Further details of these and other aspects will be apparent from the detailed description and figures included below.

DESCRIPTION OF THE DRAWINGS

Reference is now made to the accompanying figures in which:

FIG. 1 is a schematic of a gas turbine engine including multiple rotor assemblies;

FIG. 2 is a flow chart showing a method of balancing a rotor assembly of the gas turbine engine of FIG. 1 in accordance with a particular embodiment of the present invention;

FIG. 3 is a schematic showing a plot of the geometric deviation vectors when the components or a rotor assembly are arranged in initial component stacking positions relative to a first datum axis;

FIG. 4 is a schematic similar to FIG. 3, showing the same center of mass data but this time relative to a second datum defined relative to both bearings supports, to thereby provide a datum representative of the rotor centerline as defined by the two bearing supports;

FIG. 5 is an isometric view of a high pressure compressor rotor assembly of the engine of FIG. 1, showing arrows representative of example static unbalance forces in an XYZ coordinate system;

FIG. 6 is a view taken along A-A of FIG. 5, showing X and Y force components of FIG. 5 resolved from the static unbalance forces; and

FIG. 7 is a side view of the rotor assembly of FIG. 5 showing Z positions of the component centers of mass.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates a gas turbine engine 10 generally comprising, in serial flow communication, a fan 12 through which ambient air is propelled, a multistage compressor 14 for pressurizing the air, a combustor 16 in which the compressed air is mixed with fuel and ignited for generating an annular stream of hot combustion gases, and a turbine section 18 for extracting energy from the combustion gases.

Generally, the gas turbine engine 10 comprises a plurality of rotor assemblies having multiple components. For instance, in the illustrated example, the compressor 14 includes a multi-stage high pressure compressor (HPC) 22 including five stages of annular rotor components 64, 66, 68, 70 and 72. Each of the five rotor components illustrated in FIG. 1 is provided with forward and aft mounting faces (unindicated). The components are mounted face-to-face. The forward rotor component 72 has a cylindrical forward end which defines a journal for mounting a forward bearing 74. The aft rotor component 64 has a cylindrical aft end which defines a journal for mounting in an aft bearing 62. The bearings 62 and 74 support the HPC rotor assembly 22 in the engine 10. The bearings 62 and 74 define the engine centerline 76 (i.e. the axis of rotation of the rotor assembly of the HPC rotor assembly 22).

Ideally, a high pressure compressor rotor assembly, such as assembly 22 shown in FIG. 1, should be coaxially mounted with the engine centerline 76 with minimal radial eccentricity to reduce rotor imbalance during engine operation. Although each rotor component of a gas turbine engine is manufactured under very tight tolerance constraints, it remains that even the best made components are slightly off-center or out-of-balance in some respect. The effect of such slight eccentricities becomes considerable for larger components, thereby capable of causing significant radial rotor deflection and, therefore, vibration. For instance, a concentricity deviation of the mating surfaces between the two mounting ends of a rotor component may lead to an assembly unbalance if not taken into account when providing a rotor assembly including the component. Furthermore, if the axial faces at the two mounting positions of a rotor component are hot perfectly parallel to one another, a planar deviation exists which is also capable of causing a rotor assembly unbalance. Centers of masses may also be off-set from the axis of rotation, also leading to unbalance. Thus, the factors to consider are many.

It is well known that high pressure rotor assembly unbalance can be minimized by adjusting the relative circumferential positions, or stacking angle, of each component in relation to the other rotor components so as to cumulatively minimize the de-balancing effect of the concentricity deviations and the lack of squareness of the mounting ends of the rotor components. The stacking angle of each component is adjusted by rotating the component relative to an adjoining component about a datum or nominal centerline axis in the rotor stack. Therefore, the key to rotor balancing is to correctly determine what stacking angles are required to minimize unbalance.

FIG. 2 is a flowchart representing new methods, described further below, that can be used to balance the HPC rotor assembly 22 or any other rotor assembly of a gas turbine engine. The method of FIG. 2 comprises steps 30 through 48 further described below. FIGS. 3 through 14 illustrate various steps of the methods of FIG. 2 applied to the HPC rotor assembly 22.

Now referring to FIG. 2, the step 30 involves measuring the individual rotor components 64-72 for radial (concentricity) and planar (parallelism) deviation at the forward and aft mounting ends thereof, for example, using the approach described above, or any other suitable method of doing so.

As indicated in step 32 of FIG. 2, this geometric data is then used (e.g. by being provided as input to a suitable software routine, such as those already commercially-available and suitable or adaptable for such tasks) to determine initial predictions for component stacking positions based on these geometric parameters, as follows.

As shown in FIG. 3, the aft bearing 62 is selected to define a first datum 78 axis for use in stacking, the first datum being defined as a line normal to the bearing face 62 a and passing through the bearing journal or center b2. The initial predictions for assembly stacking angles, calculated in step 32, have been calculated using the measured radial and planar deviation data to minimize assembly eccentricity relative to first datum 78. (However, it will also be understood that the first datum axis 78 could instead be determined relative to the forward bearing 74). Specifically, referring again to FIG. 3, the geometric deviations of the components are represented by arrows S1-S6. The planar & radial deviations at the forward mating face of the first component 64 are measured with respect to the bearing position 62. The second component 66 is positioned/stacked relative to the first component 64 so as to offset (as much as possible) the planar and radial deviations of the first component 64 (represented by arrow S2 in FIG. 3). The third component 68 is positioned/stacked to off-set (as much as possible) the summation of planar & radial deviations of the first and second components 64, 66 combined (represented in FIG. 3 by arrows S3 and S1+S2, respectively). The initial prediction for stacking position of each subsequent component of the assembly and the forward bearing 74 is also determined in a similar fashion. A person skilled in the art will appreciate that any other suitable method of determining initial predictions for stacking positions based on the geometric data of the components of an assembly may be employed. The skilled reader will also understand that the above stacking exercise will preferably occur analytically, rather than by physically building a rotor.

Referring still to FIG. 3, center of mass data for each component is also desired. Any suitable method may be used to determine the center of mass of each component. In a preferred approach, a finite element analysis used to calculate the actual axial position (i.e. the Z dimension in FIG. 4) of the center of mass for each component, while a linear interpolation of the radial deviations of the two end point mounting positions of each component is used to calculate the radial deviations of the centers of mass. Other suitable techniques may be employed instead/as well. The radial deviations of the centers of mass of components 64-72 and the forward bearing 74 relative to first datum 78 are also calculated. FIG. 3 shows the radial deviations of the centers of mass of components 64-72 and of bearings 62 and 74 expressed graphically as interconnected points CM1 through CM7, respectively. More specifically, what is shown is the location (i.e. radial deviation) of each of the centers of mass CM1 through CM7 with respect to the first datum 78. Because it was used to define the first datum 78, the center of mass CM1 of the aft bearing 62 necessarily coincides with the first datum. The skilled reader will appreciate that the foregoing is a baseline representation of the rotor which may be obtained using conventional assembly balancing techniques and software, based upon acquired geometric deviation data. This baseline is then used in the present method, as will now be described.

Defining the first datum in this manner, however, is somewhat arbitrary. Therefore, according to the present method, it is desirable to continue the analyses to re-define the center of mass locations for all rotor components relative to a second datum which better reflects the actual centerline of rotation of the rotor assembly. Referring concurrently to FIGS. 2 and 4, the step 34 involves redefining the datum axis from first datum 78 to second datum 78′, which may be done by conceptually translating relative radial deviation data for the center of mass of the forward bearing 74 to “zero” deviation. The second datum 78′ represents the rotational axis of the bearings 62 and 74, and thus provides a second datum which may be used to balance the rotor. Thus, one translates (e.g. through the use of a suitable computer subroutine) the center of mass radial deviation data point CM7 to “align” with the second datum 78′ defined together with center of mass radial deviation data point CM1, and adjusts the points CM2 through CM6 accordingly so that they are correctly expressed relative to the new datum, as shown graphically in FIG. 4.

Any suitable manner of re-expressing the data with reference to the second datum may be used. An illustrative example of a suitable translation step can be described conceptually as “pivoting” the interconnected centers of mass CM1-CM7 about point b2 of FIG. 3 “towards” the 1st datum 78 (thus conceptually aligning datums 78 & 78′) while maintaining the relative position of the centers of mass CM1-CM7. The interconnected centers of mass CM1-CM7 are “pivoted” until CM7 reaches the datum line 78, thereby aligning the aft and forward bearings 62, 74 of the rotor assembly 60 with the datum line (representative now of axis of rotation of the assembly). The translation takes into account the axial positions of the centers of mass CM1-CM7 relative to the bearing locations b1 and b2. Axial distances from point b2 to the centers of mass CM2 to CM7 are identified by Z1, Z2, Z3, Z4, Z5 and Ztotal in FIG. 4. Thus, the translation of CM2-CM6 is proportional to the translation of CM7 to the datum line.

For example, the translation of CM6 from its “old position relative to the first datum 78 to its “new” position relative to second datum 78′, can be calculated by the following equation:

${{Rd}\; 6} = {{R\; 7} - {R\; 6\left( \frac{Z\; 5}{Ztotal} \right)}}$

where Rd6 is the new radial distance of CM6 to the second datum 78′ once CM7 has been translated to zero, R6 and R7 are the initial predictions for radial deviations of the centers of mass CM6 and CM7 relative to the first datum 78, as shown in FIG. 3, and Z5 and Ztotal are the axial distances of CM6 and CM7 respectively relative to point b2 (i.e. bearing 62).

The translation of centers of mass CM2 to CM5 relative to the centerline 76 (i.e. second datum 78′) is similarly calculated using the above equation but substituting the appropriate data respective to each center of mass. Notably, the R7 and Ztotal variables in the above equation remain constant as the intermediate components 64-72 of the rotor assembly 60 are considered with respect to the translation of the forward bearing 74 to the datum axis.

Now referring concurrently to FIGS. 2 and 5, in one aspect the method comprises determining a static unbalance mass factor, or static unbalance force of the assembly. This is done in the example presented in FIG. 2 by determining the static unbalance force for each component (step 36) and then adding the unbalances (steps 38 and 40) to acquire a total static unbalance for the rotor assembly). Steps 36-40 will now be discussed in more detail.

As mentioned, the static unbalance force associated with each component is determined (step 36 in the flow chart of FIG. 2). Thus, the static unbalance force of each of the five rotor components 64-72 between bearing 62 and 74 is determined. The radial deviation at the center of mass for each component and the component's mass are used to calculate a static unbalance force for each of the five rotor components 64-72. More specifically, this may be achieved when the “translated” radial deviations of the centers of mass CM2-CM6 of the respective components 64-72 relative to the second datum axis 78′ are multiplied by the respective component, masses to obtain five static unbalance force vectors F1-F5, as illustrated in FIGS. 5 and 6, associated respectively with the five rotor components 64-72. An XYZ coordinate system is defined in FIG. 5 to orient the component static unbalance forces F1-F5 in space. The Z axis extends axially, nominally along the rotor shaft axis, and the X and Y axes extend orthogonally radially therefrom. The direction of the static unbalance forces F1-F5 is determined by the location (i.e. radial deviation) of the centers of mass CM2-CM6 such that the force vectors passes therethrough from the datum axis 78′, and extending radially outwards (see FIG. 6). (It will be understood that the vectors F1-F5 remain within a given X-Y plane). The magnitude of each unbalance: vector corresponds to the product of the mass/weight of the rotor component and the radial deviation of its center of mass. It should be noted that throughout this application references to unbalance forces are, in the present examples, actually unbalance levels (i.e. typically expressed in units of oz-in), and thus not forces, per se. However, the skilled reader will appreciate that, once an unbalance level is determined, the resulting unbalance force is derived from the product for the unbalance and the square of the rotational speed. Consequently, it will be understood that minimizing static unbalance levels will inherently also minimizes static unbalance forces (and hence the terms unbalance and unbalance forces tend to be used interchangeably).

Next, as shown in step 38 of FIG. 2, in order to sum the individual unbalances, the X and Y magnitudes and signs (i.e. directions) of the static unbalance forces F1-F5 are resolved (step 38 in FIG. 2), so that the components of the vectors can then be summed. (Any suitable approach for summing the individual force unbalance vectors may be used.) For example, since F1-F5 are X-Y planar, the X and Y components for each static unbalance force vectors F1-F5 may be calculated and summed as follows:

Static unbalance force in the X direction Fx=Fx1+Fx2+Fx3+Fx4+Fx5

Static unbalance force in the Y direction Fy=Fy1+Fy2+Fy3+Fy4+Fy5

In step 40 of FIG. 2, the total static unbalance force of the rotor assembly is then calculated as follows:

$\begin{matrix} {{F\mspace{11mu}({total})} = {{sqrt}\mspace{11mu}\left( {{\sum{Fx}^{2}} + {\sum{Fy}^{2}}} \right)}} & {{Equation}\mspace{20mu}(1)} \end{matrix}$

Referring still to FIG. 2, balancing a rotor assembly may optionally involve the step 44 of optimizing the total static unbalance force of the rotor assembly. Any suitable optimization approach may be used. In the example described herein, optimization is achieved by iteratively considering various possible component stacking positions/angles, and determining an optimized stacking position for the components which results in the lowest rotor assembly static unbalance force (e.g. forcing F(total) of Equation (1) to zero);

The total static unbalance force acting on each of the forward and aft bearings 74 and 62 can also optionally be calculated, indicated as step 42 of FIG. 2. Any suitable manner of doing so may be used. In the example presented below, the calculation is based on the Z (axial) positions of the centers of mass of the intermediate components 64-72 relative to the Z (axial) positions of the forward and aft bearings 74 and 62, as shown in FIG. 7. The X and Y components for each static unbalance force acting on forward and aft bearings 74 and 62 are calculated and summed as follows:

Static unbalance force on forward bearings 74 (b1) in the X direction Fxb1=Fx1*Z1/Ztotal+Fx1*Z2/Ztotal+Fx3*Z1/Ztotal+Fx4*Z4/Ztotal+Fx5*Z5/Ztotal

Static unbalance force oh forward bearings 74 (b1) in the Y direction Fyb1=Fy1*Z1/Ztotal+Fy2*Z2/Ztotal+Fy1*Z3/Ztotal+Fy4*Z4/Ztotal+Fy5*Z5/Ztotal

Static unbalance force on aft bearing 62 (b2) in the X direction Fxb1=Fx1*(Ztotal−Z1)/Ztotal+Fx2*(Ztotal−Z1)/Ztotal+Fx3*(Ztotal−Z3)/Ztotal+Fx4*(Ztotal−Z4)/Ztotal+Fx5*(Ztotal−Z5)/Ztotal

Static unbalance force on aft bearing 62 (b2)in the Y direction Fyb1=Fy1*(Ztotal−Z1)/Ztotal+Fy2*(Ztotal−Z1)/Ztotal+Fy3*(Ztotal−Z3)/Ztotal+Fy4*(Ztotal−24)/Ztotal+Fy5*(Ztotal−Z5)/Ztotal

Next, the total static unbalance force acting on each of the forward and aft bearings 74 (b1) and 62 (b2) is calculated as follows:

Total static unbalance force on forward bearings 74 (b1)

Fb 1  (total) = sqrt  (∑Fxb 1² + ∑Fyb 1²)

Total static unbalance force on aft bearing 62 (b2)

Fb 2  (total) = sqrt  (∑Fxb 2² + ∑Fyb 2²)

The static unbalance forces on each bearing are thus ascertainable, as a function of axial positioning, mass and radial deviation of center of mass of the individual components. A balanced rotor may be thought of as one for which static unbalance forces on each bearing are minimized. As indicated in step 44 of FIG. 2, optionally the static unbalance forces on each bearing may be used (i.e. either with or without other techniques) to determine optimal rotor stacking angles. As mentioned, optimization may be achieved in any suitable fashion. A preferred approach is to use a suitable optimization computer program, such suitable as commercially-available optimization software, to iterate the possible combinations of component stacking angles (i.e. iterate, on possible component stacking angles such that the resulting static unbalance forces are as close to zero as possible. The output of such an optimization is preferably at least a set of component stacking angles required to achieve the optimized solution. The set of component stacking angles and/or one or more correction weights may then be provided as the rotor assembly instructions to the assembler, as will now be discussed.

Alternatively, as discussed further below, a bearing force calculation of this nature can also be used as a balance correction calculation. Adding the bearing force or unbalance calculated above to the rotor as a correction mas can result in both rotors being balanced.

As shown as step 46 in FIG. 2, the components 64-72 of the rotor assembly 60 are then physically stacked in the optimal stacking positions to thereby provide a rotor with minimal-static unbalance force, and/or minimal bearing forces, as the case may be, according to the above teachings. More specifically, the components 62-74 are assembled, preferably one by one, in sequentially order, preferably from the last compressor stage forwards. Depending on the mechanical connections provided, the rotor components may be assembled using the assembly angles rounded to the nearest bolt holes of such connections.

As mentioned, stacking the rotor preferably begins at one end, with the first component 64 being positioned in a suitable fixture. The second component 66 is positioned adjacent the mating face of the first component 64 and rotated until the angular position thereof relative to the first component 64 is optimal, according to the a set of instructions output by the above process. The remaining components 68 to 72 are stacked in a similar manner.

One will appreciate that an optimized rotor assembly will typically continue to include some deviation and unbalance. The deviation and unbalance data calculated as described above, however, may be used to guide the selection and placement of correction masses to the rotor. To achieve such a result, residual unbalance forces at the bearings are calculated and correction masses are added to (or mass suitably removed from) the assembled rotor.

In summary, presented are a number of techniques which may be used individually or in conjunction with one another (and/or other techniques) to balance a rotor assembly. The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. For example, the method of balancing described above can be applied, with suitable modification, to an overhung rotor assembly (i.e. one in which the bearings are not located at both ends). Also, any suitable approach to providing initial predictions for geometric stacking of the rotor may be used, or may be omitted altogether, with the optimization beginning instead with any selected rotor assembly stacking arrangement, Still other modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure, and such modifications are intended to fall within the appended claims. 

What is claimed is:
 1. A method of assembling a rotor assembly of a gas turbine engine having a plurality of rotor components, the rotor components being mounted for rotation between a pair of axially spaced-apart bearings defining an axis of rotation of the rotor assembly, the method comprising the steps of: for each rotor component, determining a mass and a location of a center of mass with respect to the axis of rotation of the rotor assembly; using the mass and the location of the center of mass to determine a static unbalance force associated with each rotor component; summing the static unbalance forces of the rotor components to provide a total static unbalance force of the rotor assembly, including calculating the total static unbalance force at each of the bearings; optimizing an arrangement of rotor components to thereby minimize the total static unbalance force of the rotor assembly, including optimizing the arrangement of rotor components to minimize the total static unbalance force at each of the bearings by iteratively modifying respective stacking angles of the rotor components and re-calculating the total static unbalance force until optimal stacking angles are determined; and assembling the rotor using said optimized arrangement of rotor components.
 2. The method defined in claim 1, wherein an XYZ orthogonal coordinate system is defined to orient the component static unbalance forces, the Z axis extending along the axis of rotation, the X and Y axes extending radially, and wherein determining the static unbalance force of each rotor component comprises resolving the static unbalance forces into X and Y directions.
 3. The method defined in claim 1, wherein the step of calculating the total static unbalance force at each bearing includes determining the axial positions of the centers of mass of each component relative to the bearings.
 4. The method defined in claim 1, wherein determining the location of the center of mass of the rotor components relative to the axis of rotation further comprises the steps of: establishing a first datum line defined relative to a first bearing of said pair of axially spaced-apart bearings, using geometric data of the components to determine an initial rotor assembly shape comprising initial stacking positions relative to the first datum line, defining a second datum line relative to said first bearing and a second bearing of said pair of bearings for supporting the rotor assembly, the second datum line representative of the axis of rotation of the rotor assembly, and redefining said center of mass location data of the initial stacking position of the rotor components relative to the second datum line.
 5. The method defined in claim 1, wherein determining the location of the center of mass of each rotor component comprises the steps of selecting a first bearing of said pair of axially spaced-apart bearings to define a first datum line, establishing initial component stacking positions so as to minimize component center of mass eccentricity relative to the first datum line, calculating radial deviation of the center of mass of each of the rotor components and of a location of a second bearing of said pair of bearings relative to the first datum line, and defining a second datum line through centers of both the first and second bearings by setting the radial deviation of the second bearing location to zero and then transposing the radial deviations of the rotor components relative to the second datum line.
 6. The method defined in claim 5, wherein the initial component stacking positions are determined on the basis of radial and planar deviations of the rotor components, wherein said radial and planar deviations are matched to provide a rotor assembly generally following the first datum line.
 7. The method defined in claim 6, wherein transposing the calculated radial deviations comprises: rotating the initial stacking position of the rotor assembly about the first bearing by translating the radial deviation for the center of mass of the second bearing to align with the second datum line, and adjusting the calculated radial deviations of the rotor components accordingly. 